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The Role of the Fourier Transform in Image Formation

TEM | Image Formation | BF Images | DF Images | Lattice Images (HRTEM) | ctf

Mathematically, the objective lens performs
1. a Fourier transform FT(Fourier analysis) that creates the diffraction pattern of the object in the back focal plane and
2. an inverse FT (Fourier synthesis) that makes the interference of the diffracted beams back to a real space image in the image plane (lattice image).

 

The Fourier transform (detailed mathematics) of a function ƒ(x) is defined as:

Image processing in Fourier space is performed in a similar way as image formation in the TEM:
1. the Fourier transform of an image, e.g. a HRTEM image, is calculated. Periodic structures in the image give rise to sharp spots in the resulting diffraction pattern.
2
Masks could be selected that allow only some spots or other parts of the information present in reciprocal space to contribute to the image formed by inverse FT. In TEM, similar effects are achieved by the use of aperatures.
3. A filtered image is calculated by inverse FT.

   
ETH Zürich | ETH chemistry department | ETH inorganic chemistry

modified: 6 February, 2015 by F. Krumeich | © ETH Zürich and the authors